No Valid Ramsey(5,5;42) Coloring is Circulant on Z₄₂ — Code and Data

Code and datasets accompanying the paper "No Valid Ramsey(5,5;42) Coloring is Circulant on Z₄₂: An Exhaustive Proof with Z₂₁-Bi-Circulant Search and 84-Violation Record" (Vladi Ivanov, 2026). Contents: (1) scripts/ramsey_circulant.py — exhaustive proof that no circulant on Z₄₂ or Z₄₃ is a valid Ramsey(5,5) coloring (Theorem 1 for K₄₂, Theorem 3 for K₄₃; 1,048,575 candidates each, ~8 and ~7 minutes on a single CPU core). (2) scripts/ramsey_symmetry.py — Z₂₁ bi-circulant tabu search achieving 84 monochromatic K₅ violations on K₄₂ (new record); also covers Z₇ hexa-circulant, K₄₃ bi-circulant (168v floor), and unconstrained K₄₃ search (129v record, tabu tenure 25). (3) scripts/ramsey_cayley.py — Cayley graph tabu search on all three non-cyclic groups of order 42 (D₂₁, Z₇×S₃, F₄₂); D₂₁ and Z₇×S₃ both reach 84 violations, confirming 84 as the vertex-transitive floor. (4) rust/ramsey/ — Rust unconstrained tabu solver (~4,500 iterations/sec on K₄₂, ~120× faster than Python). (5) datasets/ — Four stored colorings: three distinct 84-violation K₄₂ bi-circulant colorings and the best known 129-violation K₄₃ coloring. Each file is a JSON with fields n, s, violations, and assignment (0/1 list of length n(n−1)/2, edges in lexicographic order). (6) verify.py — one-command reviewer verification script (checks violation counts independently, reruns circulant proof slice, reproduces 84v search).